A network of brain structures including hippocampus (HC), prefrontal cortex, and striatum controls goal-directed behavior and decision making. However, the neural mechanisms underlying these functions are unknown. Here, we review the role of 'internally generated sequences': structured, multi-neuron firing patterns in the network that are not confined to signaling the current state or location of an agent, but are generated on the basis of internal brain dynamics. Neurophysiological studies suggest that such sequences fulfill functions in memory consolidation, augmentation of representations, internal simulation, and recombination of acquired information. Using computational modeling, we propose that internally generated sequences may be productively considered a component of goal-directed decision systems, implementing a sampling-based inference engine that optimizes goal acquisition at multiple timescales of on-line choice, action control, and learning.